The Experts below are selected from a list of 1524 Experts worldwide ranked by ideXlab platform
Mohamad Toutounji - One of the best experts on this subject based on the ideXlab platform.
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Morse Oscillator Propagator Using its Coherent States: Exact and Approximate
2020Co-Authors: Mohamad ToutounjiAbstract:Morse Oscillator coherent states are employed to derive an analytical expression of its off-diagonal propagator. An exact expression for the Morse Oscillator propagator is provided. Additionally, an approximately good expression is also derived. A closed-form expression of the Morse Oscillator diagonal propagator is given as well. This expression seems to be relatively easier and numerically much more stable than those in the literature. The stability issue is critical when dealing with Morse Oscillator arising dynamics and integrals as divergence becomes a lingering problem. For this reason, the presented closed-form expression of the Morse Oscillator diagonal propagator herein should be useful, especially numerically.
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Morse Oscillator propagator in the high temperature limit ii quantum dynamics and spectroscopy
2018Co-Authors: Mohamad ToutounjiAbstract:Abstract This paper is a continuation of Paper I (Toutounji, 2017) of which motivation was testing the applicability of Morse Oscillator propagator whose analytical form was derived by Duru (1983). This is because the Morse Oscillator propagator was reported (Duru, 1983) in a triple-integral form of a functional of modified Bessel function of the first kind, which considerably limits its applicability. For this reason, I was prompted to find a regime under which Morse Oscillator propagator may be simplified and hence be expressed in a closed-form. This was well accomplished in Paper I. Because Morse Oscillator is of central importance and widely used in modelling vibrations, its propagator applicability will be extended to applications in quantum dynamics and spectroscopy as will be reported in this paper using the off-diagonal propagator of Morse Oscillator whose analytical form is derived.
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Morse Oscillator propagator in the high temperature limit i theory
2017Co-Authors: Mohamad ToutounjiAbstract:Abstract In an earlier work of the author the time evolution of Morse Oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse Oscillator coherent states were employed. Morse Oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse Oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated.
Srihari Keshavamurthy - One of the best experts on this subject based on the ideXlab platform.
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local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse Oscillator
2009Co-Authors: Astha Sethi, Srihari KeshavamurthyAbstract:This work explores the possibility of controlling the dissociation of a monochromatically driven one-dimensional Morse Oscillator by recreating barriers, in the form of invariant tori with irrational winding ratios, at specific locations in the phase space. The control algorithm proposed by Huang et al. [Phys. Rev. A 74, 053408 (2006)] is used to obtain an analytic expression for the control field. We show that the control term, approximated as an additional weaker field, is efficient in recreating the desired tori and suppresses the classical as well as the quantum dissociation. However, in the case when the field frequency is tuned close to a two-photon resonance the local barriers are not effective in suppressing the dissociation. We establish that in the on-resonant case quantum dissociation primarily occurs via resonance-assisted tunneling and controlling the quantum dynamics requires a local perturbation of the specific nonlinear resonance in the underlying phase space.
Stephen Wiggins - One of the best experts on this subject based on the ideXlab platform.
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dynamics of the Morse Oscillator analytical expressions for trajectories action angle variables and chaotic dynamics
2019Co-Authors: Vladimir Krajňak, Stephen WigginsAbstract:We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the “Morse Oscillator”). We use the geometry of the level sets to construct explicit express...
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dynamics associated with a quasiperiodically forced Morse Oscillator application to molecular dissociation
1992Co-Authors: Darin Beigie, Stephen WigginsAbstract:The dynamics associated with a quasiperiodically forced Morse Oscillator is studied as a classical model for molecular dissociation under external quasiperiodic electromagnetic forcing. The forcing entails destruction of phase-space barriers, allowing escape from bounded to unbounded motion. In contrast to the ubiquitous Poincare map reduction of a periodically forced system, we derive a sequence of nonautonomous maps from the quasiperiodically forced system. We obtain a global picture of the dynamics, i.e., of transport in phase space, using a sequence of time-dependent two-dimensional lobe structures derived from the invariant homoclinic tangle of a persisting invariant saddle-type torus in a Poincare section of an associated autonomous system phase space. Transport is specified in terms of two-dimensional lobes mapping from one to another within the sequence of lobe structures, and this provides the framework for studying basic features of molecular dissociation in the context of classical phase-space trajectories. We obtain a precise criterion for discerning between bounded and unbounded motion in the context of the forced problem. We identify and measure analytically the flux associated with the transition between bounded and unbounded motion, and study dissociation rates for a variety of initial phase-space ensembles, such as an even or weighted distribution of points in phase space, or a distribution on a particular level set of the unperturbed Hamiltonian (corresponding to a quantum state). A double-phase-slice sampling method allows exact numerical computation of dissociation rates. We compare single- and two-frequency forcing. Infinite-time average flux is maximal in a particular single-frequency limit; however, lobe penetration of the level sets of the unperturbed Hamiltonian can be maximal in the two-frequency case. The variation of lobe areas in the two-frequency problem gives one added freedom to enhance or diminish aspects of phase-space transport on finite time scales for a fixed infinite-time average flux, and for both types of forcing the geometry of lobes is relevant. The chaotic nature of the dynamics is understood in terms of a traveling horseshoe map sequence.
Emanuel F De Lima - One of the best experts on this subject based on the ideXlab platform.
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effects of Oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse Oscillator
2012Co-Authors: Emanuel F De Lima, Egydio R De CarvalhoAbstract:Abstract The role of the spatial dependence of dipole coupling on the dissociation dynamics of the classical driven Morse Oscillator is investigated, in particular, the effects of Oscillatory behavior of the dipole function are considered. The initial conditions for the calculations are chosen to correspond to highly excited vibrational states, which are close to the Morse potential separatrix. It is shown that the Oscillatory form of the dipole function influences the splitting of the separatrix and accordingly the dissociation dynamics. Specifically, the dipole Oscillatory behavior can prevent trajectories from escaping the potential well and consequently inhibiting the dissociation mechanism. It is found that this inhibition of dissociation is related to the change of sign of the dipole function.
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control of chaotic photoassociation in the driven Morse Oscillator
2011Co-Authors: Emanuel F De LimaAbstract:This work explores the control of photoassociation in the classical driven Morse Oscillator by means of bichromatic pulses. The ensemble of initial conditions is chosen as a Gaussian distribution in order to mimic corresponding quantum calculations. The fraction of photoassociated trajectories is investigated as a function of the parameters of the external fields. Attention is given to the role played by the relative phase of the two fields. It is found that the relative phase can be used to control photoassociation yield.
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the Morse Oscillator under time dependent external fields
2006Co-Authors: Emanuel F De Lima, Jose Eduardo Martinho HornosAbstract:A method to solve the equations for the Morse Oscillator under intense time-dependent external fields is presented. Exact analytical formulas for the dipole matrix elements are calculated by the use of the hypergeometric algebra. The continuum is described by an expansion using Laguerre functions. The full algorithm for the calculation of wave functions can be controlled by the convergence of series and by the errors of a first order integration method. We apply our technique to the selective preparation of high overtones by femtosecond laser pulses. The population of the target state is optimized as a function of the intensity and frequency. Introducing a second simultaneous laser, we study the effects of relative frequency and phase over the target state population and dissociation channels. The calculations exhibit a rich interference pattern showing the enhancement and the suppression of the target population by varying the laser parameters.
Astha Sethi - One of the best experts on this subject based on the ideXlab platform.
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local phase space control and interplay of classical and quantum effects in dissociation of a driven Morse Oscillator
2009Co-Authors: Astha Sethi, Srihari KeshavamurthyAbstract:This work explores the possibility of controlling the dissociation of a monochromatically driven one-dimensional Morse Oscillator by recreating barriers, in the form of invariant tori with irrational winding ratios, at specific locations in the phase space. The control algorithm proposed by Huang et al. [Phys. Rev. A 74, 053408 (2006)] is used to obtain an analytic expression for the control field. We show that the control term, approximated as an additional weaker field, is efficient in recreating the desired tori and suppresses the classical as well as the quantum dissociation. However, in the case when the field frequency is tuned close to a two-photon resonance the local barriers are not effective in suppressing the dissociation. We establish that in the on-resonant case quantum dissociation primarily occurs via resonance-assisted tunneling and controlling the quantum dynamics requires a local perturbation of the specific nonlinear resonance in the underlying phase space.